SOLUTION: This is for differential equations, topic is about separation of variables. Find the general and particular solution of the given. 1.) y' + y = 5sin2x 2.) y' + 3y = x + e^-

Algebra ->  Equations -> SOLUTION: This is for differential equations, topic is about separation of variables. Find the general and particular solution of the given. 1.) y' + y = 5sin2x 2.) y' + 3y = x + e^-      Log On


   

Question 1187735: This is for differential equations, topic is about separation of variables.
Find the general and particular solution of the given.
1.) y' + y = 5sin2x
2.) y' + 3y = x + e^-2x at x=0 and y=1
Thank you so much.
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!




First-order linear ODE:

Let



Note that



Use the reverse product rule:





Left side:



Right side:



Integrate by parts twice:

Let and

Then and , so



Integrate by parts a second time to obtain:



Then add to both sides



And divide by 5



Therefore:



Divide by



You did not give initial conditions with this one, so there is only a general solution.

John

My calculator said it, I believe it, that settles it

From
I > Ø